# Kalman filter for time series prediction

I have the information about the behaviour of 400 users across period of 1 months (30 days). Across those 30 days I measure 4 different information (let's call it A,B,C and D), hence I have a total of 4 time series. My goal is to predict, starting from day 5, the future values of A, by knowing the past values of A, B, C and D. So:

A(5) = f(A(1,2,3,4), B(1,2,3,4), C(1,2,3,4), D(1,2,3,4))

Ideally, I'd like to estimate the whole future values, from day 5 to day 30.

I tried to use LSTM by using as input the past series, to predict the future trends. However, I am not getting great results, and I am hoping I can use a simpler approach. I came across with the concept of Kalman Filter, where the value at time step k can be estimated by using the past values. Here there are some nice examples , however I have no idea where to start from. Would it fit with my problem, if yes, how could I fit my past values into the equation for the estimation of A(k)? Any suggestion is appreciated.

• Kalman filters require a model apriori. Which is why it is step #1 in your link. The model is used to predict future outputs. Since models are never perfect, the filter is used to keep the model state from drifting too far from reality. But you need a model first. Nov 29 '17 at 14:07

Example To put this in context, consider that we want to predict position $$x_k$$. We know from high school physics that $$x_k = x_{k-1}+v_k\delta t,$$ where $$v$$ is the velocity, $$k$$ the discrete time index and $$\delta t$$ the discrete time step. So we have a model. To make use of the Kalman Filter, we also need measurements, e.g. for position and/or velocity (you have this one).